Moar Math!

You may have noticed that, in a number of recent posts, the topic has been math. The good-bad news is that there’s more to come (sorry, but I love this stuff). The good-good news is that I’m done with math foundations. For now.

To wrap up the discussion of math’s universality and inevitability — and also of its fascination and beauty — today I just have some YouTube videos you can watch this Sunday afternoon. (Assuming you’re a geek like me.)

So get a coffee and get comfortable!

To start, here’s a pretty good TED talk that touches on many of the topics from the recent posts:

Here’s another from one of my favorite YouTube channels, Numberphile, that talks about three basic philosophical positions mathematicians take regarding the ontology of math: Platonism, Nominalism, and Fictionalism.

You might think of these, essentially, as: Believer, Agnostic, Atheist positions with regard to the reality of numbers. (Note that, other than Platonism, these are broad philosophical positions that extend beyond mathematics.)

This next video has a slightly poorer quality than the first two, but it’s worth watching if for no other reason than the speaker’s enthusiasm regarding math.

Much of the fascination and love of math is based on its surprising beauty and elegance. It is the purest of the sciences and has the strongest elements from a priori experience.

Here’s a video that explores the important difference between the transcendental numbers and all the rest that aren’t. Even irrational real numbers have an algebraic expression (√2, for example), but transcendental ones do not.

The video also touches briefly on Euler’s Formula.

The game of reducing an expression to zero is fascinating!

To wrap up, here’s video about math, sex, love, the human mind, and a bit more. It may also change your mind about what a mathematician looks like:

In the posts ahead, I’m going to explore the complexity of computers and the human brain. It’s all leading to a discussion about whether consciousness is likely to be algorithmic or not and what it might take to build an “artificial” mind. Along the way I’ll be referring back to some of this math foundation stuff.

Not that there might not be some diversions along the way. (Or do I mean divisions? After all that math, it’s hard to tell.)

I have seen a post or two and I do like it. I am still studying to become an electronic engineer. Hmm, I have always like Math ever since I was a kid. I loved how it has always appeared as a challenge to me, riddle to be solved. I’m currently balancing on both ends of my pole – blogging and studying. 🙂

EE would be a good major; hard to think electronics will ever be obsolete. (One bit of unsought advice: The better your foundation and theory skills, the better you can adapt to changing technology. The more you focus on one area, the more you risk that area going out of style.)

One of my first loves was electronics! As a kid I taught myself how vacuum tubes worked only to discover the world had moved on to transistors. I spent years trying to understand solid state physics with all that valance band stuff, but never really got it. It was only when I looked at transistors functionally, in terms of base current and emitter current, that the light bulb finally went on and I could design circuits with them…

Only to find the world had moved on to integrated chips. But digital logic turned out to be so much easier. Stuff was either on or off. I was never much good with analog circuits, especially high frequency stuff where everything is an inductor and a capacitor. RF is hard! Of course, once I had the logic chips down, ta da, now it’s all bloody microprocessors, so I start all over again.

But that did lead to computer programming, and I made the jump from hardware to software. How many computer programmers does it take to change a light bulb? None. That’s hardware! 😀

For many, science is cool because it provides clear, objective answers — a form of truth not often found in the social world. Math is the purest science, so it’s the most clear, the most objective, and provides the clearest truths. It is also fascinating and elegant and often beautiful. Plus it’s so fundamental to reality and describes so much of it so nicely.